Inverse obstacle scattering problems with a single incident wave and the logarithmic differential of the indicator function in the Enclosure Method

Abstract

This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the indicator function in the Enclosure Method. The previous indicator function is essentially real-valued since only its absolute value is used. In this paper, another method for the use of the indicator function is introduced. The method employs the logarithmic differential with respect to the independent variable of the indicator function and yields directly the coordinates of the vertices of the convex hull of unknown polygonal sound-hard obstacles or thin ones. The convergence rate of the formulae is better than that of the previous indicator function. Some other applications of this method are also given.

submitted to Inverse Problems on April 4, 2011. 26 pages

References in corpus (4)

• On reconstruction in the inverse conductivity problem with one measurement
• The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval
• The Herglotz wave function, the Vekua transform and the enclosure method
• A note on the enclosure method for an inverse obstacle scattering problem with a single point source

Cited by in corpus (4)

• Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a finite time interval
• Extracting discontinuity using the probe and enclosure methods
• New Development of the Enclosure Method for Inverse Obstacle Scattering
• Reconstruction of a source domain from the Cauchy data: II. Three dimensional case